Almost split sequences for Knorr lattices

TL;DR

This paper explores properties of almost split sequences in the stable category of group lattices over a complete discrete valuation ring, providing criteria for indecomposability and characterizing endomorphism rings.

Contribution

It introduces new criteria for indecomposability of middle terms and characterizes stable endomorphism rings of Heller lattices in the context of Knorr lattices.

Findings

Necessary and sufficient conditions for indecomposability of middle terms.

Characterization of stable endomorphism rings of Heller lattices.

Applications of adjunctions in the stable category of OG.

Abstract

Let $O$ be a complete d.v.r. and $G$ a finite group. We give two applications of an adjunction in the stable category of $OG$. The first application gives necessary and sufficient conditions for the middle term of an almost split sequence terminating in a Knorr lattice to be indecomposable. The second characterises the stable endomorphism rings of Heller lattices of kG-modules.